There must be something wrong here. This thread named "An inhomogenous equation-help !" surely was posted by me. I do not understand why it is mixed with the thread by mremilli, who posted long before me. I might have made a mistake when posting this one mightn't I?

The fact that the equation is not homogeneous is no big deal but it will simplify a lot if you find a function that satisfies just the boundary conditions. Subtract that from u to get a differential equation that is still non-homogeneous but does have homogeneous boundary conditions. You can then write the solution as a Fourier sine series.